Is it possible to simulate tape measure bending with Soft Body physics?
Plastic deformation &amp; Stiff quads



I made several changes to the provided Blendfile to achieve this result.

I'll try to summerize them focusing on the most important ones in a qualitative way, as to make a simulation look good what matter is the "whole":


Stiff quads should be enabled. The option will add to the face a "skew resistance", as material elements in the real world have. This way we ensure that the tape has more chanches of keeping his shape
Springs strenght increased (almost 1). Metal have quite big elastic deformations compared to other materoals, but the deformation of the elements at the simulation's scale is almost none, so we should make the springs between the faces as rigid as we can.
Spring Damp lowerd (and Goal Dampening too). Arbitrary dampening factors usually kills the simulation features in favor of its stabilty. I would generally try to keep them as low as possible.
Some Bending resistance. As you already did, must be present in order to give some consistency to the structure.
High Plastic Deformation factor. This is probably the key of the whole simulation. While the other feature were all made to give resistance to the tape, this is what brings it to the "breaking point". If enabled, each polygon will keep the occured deformation. Step by step, the structure is falling, bending the wings of the truss toward the outside, lowering the momentum of inertia of the section in the area near the fixed part, till it became so little that the section cant' resist anymore and the section becomes a hinge.


Other minor changes:


Geometry of the object (shorter and more compact section)
Resolution of the object (less polygon to have more control upon them and faster baking time :P )
Mass of the Soft Body.
Initial rotation of the bar (15°) (to increase the folding visibility)
Post simulation modifier &amp; Matcap... for "beauty's sake"